Joint Bayesian inversion for analyzing conservative and reactive breakthrough curves

We present a joint Bayesian inverse method for analyzing conservative and reactive tracer data, which estimates non-parametric transfer functions and effective first-order reaction rate coefficients simultaneously. A stochastic sampling approach based on Markov Chain Monte Carlo (MCMC) methods was used to simulate samples from the posteriors, with a Metropolis within Gibbs sampler used for transfer functions and reaction rate coefficients. Non-negativity constraints were realized by choosing a reflected Gaussian prior for the transfer function and a lognormal prior for the reaction rate coefficient. The approach was tested by synthetic sparse datasets with introduced normal random errors or periodic errors, and then it was applied to the tracer test data collected at Oak Ridge National Laboratory. The results indicate that the developed approach was well capable of characterizing anomalous transfer functions, such as multi-modal functions, and quantifying the uncertainty of both transfer functions and reaction rate coefficients. In particular, compared with the approach of individual inversion of sparse data, the joint inversion approach taking advantage of the sharing of information regarding transport processes across the conservative tracer and reactive tracer data leads to the improved estimation of transfer functions and reaction rate coefficients for sparse datasets.